Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays

Josef Diblík, Blanka Morávková
2014 Abstract and Applied Analysis  
The purpose of this paper is to develop a method for the construction of solutions to initial problems of linear discrete systems with constant coefficients and with two delaysΔx(k)=Bx(k-m)+Cx(k-n)+f(k),wherem,n∈ℕ,m≠n,are fixed,k=0,...,∞,B=(bij),C=(cij)are constantr×rmatrices,fis a givenr×1vector, andxis anr×1unknown vector. Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential for two delays. Such approach results in a possibility to express
more » ... ibility to express an initial Cauchy problem in a closed form. Examples are shown illustrating the results obtained.
doi:10.1155/2014/320476 fatcat:m35f4syclfcbjd3jutlxikesdq